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In episode 31, we were in the middle of the fight between Hien and Senkuu which ends with Hien dying and Genji Togashi preparing to take his place in the fight.

Suddenly we are shown Tazawa and Matsuo who survived the fall in the river and met the principle Edajima Heihachi who tells them that they are in the middle of the 4th battle.

This is followed by a brief summary of the missed fights in a short time.

Why did they skip the battles and fast forward to the final battle between Momotarou and Daigouin Jaki?

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Because the anime got canceled while in the middle of broadcasting due to receiving continuing protest from Parent-Teacher Association (PTA) in Japan.

From Japanese Wikipedia,

アニメ独自の解釈が折り込まれているが、放送当初からPTAの抗議が絶えず、中盤以降は放送取り止めを叫ぶほどに激化したという。結局、大威震八連制覇編で放送は終了することになり、第31話にて第2戦途中から最終対決までの経過をダイジェストで進める強引な手法が採られている。

While the original interpretation of the anime was folded in, PTA's protest continued since from the beginning of the broadcast, then got intensified until reaching to the point of "shouting" to stop the broadcast while in the middle of the story plot. In the end, since the broadcast was decided to end after "Great Trembling Conquest of the Unified Eight" arc, the battle from the middle of 2nd round until the final round in episode 31 was cut and summarized heavily to advance the progress.

(Emphasize mine)

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